论文标题
使用Bell表达式的Hilbert空间维度独立于设备的依赖性认证
Device-independent certification of Hilbert space dimension using a family of Bell expressions
论文作者
论文摘要
Dimension证人提供了独立于设备的认证，以对重现观察到的数据所需的最小维度，而不对用于生成实验统计的设备的功能施加假设。 In this paper, we provide a family of Bell expressions where Alice and Bob perform $2^{n-1}$ and $n$ number of dichotomic measurements respectively which serve as the device-independent dimension witnesses of Hilbert space of $2^{m}$ dimensions with $m=1,2..2^{\lfloor n/2\rfloor}$.这里考虑的贝尔表达式的家族决定了通信游戏的成功概率，称为$ n $ bit-bit-bit-bit-pollivious随机访问代码。在操作理论的本体论模型中，均等遗忘的约束等效于制备非上下文性假设。对于任何给定的$ n \ geq 3 $，如果对随机访问代码的编码方案施加了这样的约束，则贝尔表达式的局部界限将减少到制备非上下文界限。我们为$ n = 4,5 $案例提供明确的示例，以证明相关的钟表表达式证明了量子和两个Qubit System，并且对于$ n = 6 $ case，相关的铃铛表达式证明了值，两倍和三Qubit的系统。我们进一步证明了依次通过多个鲍勃的量子准备上下文共享，以检查共享制备上下文的鲍勃数量是否取决于系统的维度。我们提供了$ n = 5 $和$ 6 $的明确示例，以证明对$ 2^{m} $ dimensional Systems中的任何一个bobs依次共享上下文的数量保持不变。
Dimension witness provides a device-independent certification of the minimal dimension required to reproduce the observed data without imposing assumptions on the functioning of the devices used to generate the experimental statistics. In this paper, we provide a family of Bell expressions where Alice and Bob perform $2^{n-1}$ and $n$ number of dichotomic measurements respectively which serve as the device-independent dimension witnesses of Hilbert space of $2^{m}$ dimensions with $m=1,2..2^{\lfloor n/2\rfloor}$. The family of Bell expressions considered here determines the success probability of a communication game known as $n$-bit parity-oblivious random access code. The parity obliviousness constraint is equivalent to preparation non-contextuality assumption in an ontological model of an operational theory. For any given $n\geq 3$, if such a constraint is imposed on the encoding scheme of the random-access code, then the local bound of the Bell expression reduces to the preparation non-contextual bound. We provide explicit examples for $n=4,5$ case to demonstrate that the relevant Bell expressions certify the qubit and two-qubit system, and for $n=6$ case, the relevant Bell expression certifies the qubit, two-qubit and three-qubit systems. We further demonstrate the sharing of quantum preparation contextuality by multiple Bobs sequentially to examine whether number of Bobs sharing the preparation contextuality is dependent on the dimension of the system. We provide explicit example of $n=5$ and $6$ to demonstrate that number of Bobs sequentially sharing the contextuality remains same for any of the $2^{m}$ dimensional systems.
